Japanese laid-open patent publication No. 4-168603 for example, describes a magnetic recording and reproducing system for magnetically recording and reproducing a digital image signal by image compression. According to this magnetic recording and reproducing system, it becomes possible to record a digital image signal for a long time by properly selecting an amount of information of the digital image signal and density with which the digital image signal is recorded on a magnetic tape.
Further, an input digital image signal is converted by a blocking circuit to data of block unit composed of a plurality of pixel data. Output data from the blocking circuit is compression-coded by a coding circuit. An output from the coding circuit is supplied through a channel coding circuit to a magnetic head and thereby recorded on the magnetic tape.
As an example of the block coding circuit, there is proposed a block coding circuit in which pixel data of each block is processed in a DCT (discrete cosine transform) fashion, coefficient data thus obtained by DCT is quantized and quantized data is compression-coded by run-length Huffman coding.
In a bit rate reduction VTR (video tape recorder), calculation error occurs at three portions, which will be described below with reference to FIG. 1.
As shown in FIG. 1 of the accompanying drawings, calculation error occurs at three portions, i.e., a discrete cosine transform (DCT) circuit 2, a quantization (Q) circuit 3 and an inverse discrete cosine transform (IDCT) circuit 9 as shown by reference symbols ".epsilon.".
The DCT circuit 2 will be considered initially. The DCT circuit 2 performs calculation of trigonometric function, and a calculated result of the DCT circuit 2 is given by an irrational number. Therefore, when the calculated result is rounded by a finite bit rate, a calculation error occurs. When a calculated result N bits of the DCT circuit 2 are rounded by 12 bits, a calculation error occurs.
An output from the DCT circuit 2 is quantized by the quantization circuit 3 and thereby suppressed to data of a predetermined data amount. A bit rate obtained at that time is changed with a quantization step size. For example, the bit rate changes in a range of from 11 bits (maximum) to 1 bit (minimum). Specifically, assuming that M is the bit rate, then M changes in a range of from 1 to 11 bits. Therefore, a calculation error occurs.
When the digital image signal is reproduced, if the digital image signal is rounded to 8 bits after it had been processed in an IDCT fashion, then a calculation error occurs.
As shown in FIG. 1, a calculation error does not occur in a variable length coding (VLC) circuit 4, a variable length decoding (VLD) circuit 7 and an inverse quantization (Q-.sup.1) circuit 8.
Accumulation of calculation errors caused by the rounding system is not a serious problem so long as the digital image signal is compressed and expanded only one time. However, when the VTR is in use, it is customary that recorded contents on the magnetic tape are dubbed. Thus, a picture quality obtained in a so-called multi-generation (picture recorded when dubbing is made several times) becomes an important factor. Particularly, when the digital image signal is repeatedly compressed and expanded according to the same algorithm, a calculation error is accumulated in the same direction, which causes a problem that can not be neglected.
A rounding circuit used in this kind of apparatus is based on the rounding-off. Therefore, when numeral placed after omitted bits (digits) (i.e., placed after the decimal point) are 0.5, there occurs a maximum calculation error. In this case, a numeral is rounded to an integer of which absolute value is larger.
Let it be considered that the digital image signal is dubbed by a bit rate reduction VTR, for example. In this case, it is unavoidable that the digital image signal is repeatedly compressed and expanded each time dubbing is made. As a result, according to the ordinary rounding-off, a rounding error is accumulated each generation of dubbing (i.e., each time dubbing is made), thereby a picture quality being deteriorated.
The reason for this is that, each time the digital image signal is compressed and expanded, DCT coefficient and image data whose numeral is 0.5 in decimal notation is generated. In concurrently therewith, the numeral is rounded to an integer whose absolute value is larger.
As a consequence, a calculation error is accumulated in the same direction so that perceptible block distortion, such as direct current (DC) level shift or the like occurs. Although it is frequently observed that this error is converged when dubbing is carried our several times, i.e., deterioration of a picture quality does not proceed any more, in worst cases, a calculation error is accumulated infinitely each time dubbing is made.
Furthermore, when an inner calculation accuracy is not sufficient, an influence exerted by a rounding error becomes more remarkable. The reason for this is that, the probability that DCT coefficient or image data of 0.5 will occur becomes large as the inner calculation accuracy is lowered. As a result, a convergence of accumulated error is delayed.